y using the sphencal cordinates, find Solid Gboun ded by Qnd abave by tle centraid 6f...
Find the volume of the solid Use spherical coordinates to find the mass of the solid bounded below by the cone z=« .) and above by the sphere x+y+ =9if its density is given by 8(x,y,2) = x+ y+Z. JC Use spherical coordinates to find the mass of the solid bounded below by the cone z=« .) and above by the sphere x+y+ =9if its density is given by 8(x,y,2) = x+ y+Z. JC
1. Using polar coordinates in the x-y plane, find the volume of the solid above the cone z r and below the hemisphere z= v8-r2. As a check the answer is approximately 13.88 but of course you have to calculate the exact answer 2. At the right is the graph of the 8-leafed rose r 1+2cos(40) Calculate the area of the small leaf. As a check the answer is 0.136 to 3 places of decimal (But of course you have...
Find the volume of the given solid region bounded below by the cone z = \x² + y2 and bounded above by the sphere x2 + y2 + z2 = 8, using triple integrals. (0,0,18) 5) 1 x? +y? +22=8 2-\x?+y? The volume of the solid is (Type an exact answer, using a as needed.)
1. Find the volume of the solid under the cone z= sqrt (x^2 + y^2) and over the ring 4 |\eq x^2 + y^2 |\eq 25. 2. Find the volume of the solid under the plane 6x + 4y + z= 12 and over the disk with border x^2 + y^2 = y. 3. The area of the smallest region, locked by the spiral r\Theta= 1, the circles r=1 and r=3 and the polar axis.
Find the volume of the solid of revolution using the method that best fits. Y = X?, X = y2 about y=1
Use cylindrical coordinates to find the mass of the solid Q of density ρ.Q={(x, y, z): 0 ≤ z ≤ 9-x-2 y, x²+y² ≤ 25} ρ(x, y, z)=k \sqrt{x²+y²}Use cylindrical coordinates to find the indicated characteristic of the cone shown in the figure.Assume that the density of the cone is ρ(x, y, z)=k \sqrt{x²+y²} and find the moment of inertia about the z-axis.
Using any method find the volume of the solid between the surfaces z= 8 – y² and z = 22 + y2
3. Find the volume of the solid in the first octant that lies above the cone z = 13(x+ + y) and inside the sphere x2 + y2 + y2 = 42. Use spherical coordinates. 4. Determine if the vectorfield F(x, y) - (x + y)i + (2xy + y) is conservative If it is, find a potential function
3. Find the volume of the solid in the first octant that lies above the cone z = 3(x + y) and inside the sphere x2 + y2 + z2 = 42. Use spherical coordinates.
F. ds where F = (1, y, z) and E is given by the solid ice cream cone bounded by a = c2 + y2 and r? + y2 + 2 = 1. Use the Divergence Theorem to find | SF